## Regression models of placement outcomes
library(tidyverse)
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library(cowplot)
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library(broom)
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library(forcats)
library(rstanarm)
## Loading required package: Rcpp
## Warning: package 'Rcpp' was built under R version 3.5.2
## rstanarm (Version 2.18.2, packaged: 2018-11-08 22:19:38 UTC)
## - Do not expect the default priors to remain the same in future rstanarm versions.
## Thus, R scripts should specify priors explicitly, even if they are just the defaults.
## - For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores())
## - Plotting theme set to bayesplot::theme_default().
options(mc.cores = parallel::detectCores() - 2)
## bayesplot makes itself the default theme
theme_set(theme_minimal())

library(tictoc)
library(assertthat)
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## Attaching package: 'assertthat'
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##     has_name
## Suppress messages when generating HTML file
knitr::opts_chunk$set(message = FALSE)

source('../R/predictions.R')
source('../R/posterior_estimates.R')
data_folder = '../data/'
output_folder = '../output/04_'
paper_folder = '../paper/'

# cluster_distances = read_csv(str_c(data_folder, 
#                                    '00_k9distances_2019-03-15.csv')) %>% 
#     count(cluster = cluster, average_distance = avgDist) %>% 
#     mutate(cluster = as.character(cluster))
# 
# ggplot(cluster_distances, aes(cluster, scale(average_distance))) +
#     geom_label(aes(label = n, fill = n, size = n), color = 'white')

load(str_c(data_folder, '02_parsed.Rdata'))
univ_df = read_rds(str_c(data_folder, '03_univ_net_stats.rds')) #%>% 
    # left_join(cluster_distances)

individual_df = individual_df %>%
    left_join(univ_df, by = c('placing_univ_id' = 'univ_id')) %>%
    ## Use the canonical names from univ_df
    select(-placing_univ) %>%
    ## Drop NAs
    # filter(complete.cases(.))
    filter_at(vars('permanent', 'aos_category', 
                   'graduation_year', 'prestige', 
                   'community', 'cluster_label',
                   'gender', 'frac_w', 
                   'frac_high_prestige', 'total_placements'), 
              all_vars(negate(is.na)(.))) %>%
    rename(cluster = cluster_label) %>% 
    mutate(perc_w = 100*frac_w, 
           perc_high_prestige = 100*frac_high_prestige)

## Variables to consider: aos_category; graduation_year; placement_year; prestige; out_centrality; cluster; community; placing_univ_id; gender; country; perc_w; total_placements


## Giant pairs plot/correlogram ----
## perc_high_prestige, out_centrality, and prestige are all tightly correlated
## All other pairs have low to moderate correlation
individual_df %>% 
    select(permanent, aos_category, aos_diversity, perc_high_prestige,
           graduation_year, placement_year, prestige, 
           in_centrality, out_centrality, community, 
           cluster, #average_distance,
           gender, country, perc_w, 
           total_placements) %>% 
    mutate_if(negate(is.numeric), function(x) as.integer(as.factor(x))) %>% 
    mutate_at(vars(in_centrality, out_centrality), log10) %>% 
    # GGally::ggpairs()
    cor() %>% 
    as_tibble(rownames = 'Var1') %>% 
    gather(key = 'Var2', value = 'cor', -Var1) %>% 
    ggplot(aes(Var1, Var2, fill = cor)) +
    geom_tile() +
    geom_text(aes(label = round(cor, digits = 2)), 
              color = 'white') +
    scale_fill_gradient2()

## No indication that AOS diversity has any effect
ggplot(individual_df, aes(aos_diversity, 1*permanent)) + 
    geom_point() +
    geom_smooth(method = 'loess')

## And not for fraction of PhDs awarded to women women, either
ggplot(individual_df, aes(frac_w, 1*permanent)) +
    geom_point() +
    geom_smooth(method = 'loess')

## Descriptive statistics ----
## Individual-level variables (all discrete)
desc_1_plot = individual_df %>%
    select(permanent, aos_category, 
           graduation_year, placement_year, 
           gender) %>%
    gather(key = variable, value = value) %>%
    count(variable, value) %>% 
    mutate(variable = str_replace_all(variable, '_', ' ')) %>% 
    ggplot(aes(fct_rev(value), n, group = variable)) +
    geom_col(aes(fill = variable), show.legend = FALSE) +
    scale_fill_brewer(palette = 'Set1') +
    xlab('') +
    coord_flip() +
    facet_wrap(vars(variable), scales = 'free', ncol = 3)
## Warning: attributes are not identical across measure variables;
## they will be dropped
desc_1_plot

ggsave(str_c(output_folder, 'descriptive_1.png'), 
       desc_1_plot, 
       height = 2*2, width = 2*3, scale = 1.5)

## Program-level categorical
desc_2_plot = individual_df %>%
    select(prestige, country, 
           community, cluster) %>%
    gather(key = variable, value = value) %>%
    count(variable, value) %>% 
    ggplot(aes(fct_rev(value), n, group = variable)) +
    geom_col(aes(fill = variable), show.legend = FALSE) +
    scale_fill_viridis_d() +
    xlab('') +
    coord_flip() +
    facet_wrap(vars(variable), scales = 'free', ncol = 3)
desc_2_plot

ggsave(str_c(output_folder, 'descriptive_2.png'), 
       desc_2_plot, 
       height = 2*2, width = 2*2, scale = 1.5)

## Program-level continuous variables
# individual_df %>%
#     select(frac_w, total_placements, perm_placement_rate) %>%
#     gather(key = variable, value = value) %>%
#     group_by(variable) %>%
#     summarize_at(vars(value), 
#                  funs(min, max, mean, median, sd), 
#                  na.rm = TRUE)

program_cont = individual_df %>% 
    mutate(in_centrality = log10(in_centrality)) %>% 
    select(`women share` = frac_w, 
           `total placements` = total_placements, 
           `permanent placement rate` = perm_placement_rate, 
           `AOS diversity (bits)` = aos_diversity,
           `hiring centrality (log10)` = in_centrality) %>% 
    gather(key = variable, value = value)

desc_3_plot = ggplot(program_cont, aes(value)) +
    geom_density() +
    geom_rug() +
    geom_vline(data = {program_cont %>% 
            group_by(variable) %>% 
            summarize(mean = mean(value))}, 
            aes(xintercept = mean, 
                color = 'mean')) +
    geom_vline(data = {program_cont %>% 
            group_by(variable) %>% 
            summarize(median = median(value))}, 
            aes(xintercept = median, 
                color = 'median')) +
    scale_color_brewer(palette = 'Set1', 
                       name = 'summary\nstatistic') +
    facet_wrap(~ variable, scales = 'free', ncol = 3) +
    theme(legend.position = 'bottom')
desc_3_plot

ggsave(str_c(output_folder, 'descriptive_3.png'), 
       desc_3_plot, 
       height = 2*2, width = 2*3.5, scale = 1.5)

plot_grid(desc_1_plot, 
          desc_2_plot, 
          desc_3_plot, 
          align = 'v', axis = 'lr', ncol = 1, 
          labels = 'AUTO',
          hjust = -2
          )

ggsave(str_c(output_folder, 'descriptive.png'), 
       height = 6.5*2, width = 4*2, scale = 1.5)
ggsave(str_c(paper_folder, 'fig_descriptive.png'), 
       height = 6.5*2, width = 4*2, scale = 1.5)



## Model -----
model_file = str_c(data_folder, '04_model.Rds')
if (!file.exists(model_file)) {
    ## ~700 seconds
    tic()
    model = individual_df %>% 
        mutate(prestige = fct_relevel(prestige, 'low-prestige'), 
               country = fct_relevel(country, 'U.S.')) %>% 
        stan_glmer(formula = permanent ~ 
                       (1|aos_category) +
                       gender + 
                       (1|graduation_year) +
                       (1|placement_year) +
                       1 +
                       aos_diversity +
                       (1|community) +
                       (1|cluster) +
                       # average_distance +
                       log10(in_centrality) +
                       total_placements +
                       perc_w +
                       country +
                       prestige,
                   family = 'binomial',
                   ## Priors
                   ## Constant and coefficients
                   prior_intercept = cauchy(0, 2/3, autoscale = TRUE), ## constant term + random intercepts
                   prior = cauchy(0, 2/3, autoscale = TRUE),
                   ## error sd
                   prior_aux = cauchy(0, 2/3, autoscale = TRUE),
                   ## random effects covariance
                   prior_covariance =  decov(regularization = 1, 
                                             concentration = 1, 
                                             shape = 1, scale = 1),
                   seed = 1159518215,
                   adapt_delta = .99,
                   chains = 4, iter = 4000)
    toc()
    write_rds(model, model_file)
} else {
    model = read_rds(model_file)
}

prior_summary(model)
## Priors for model 'model' 
## ------
## Intercept (after predictors centered)
##  ~ cauchy(location = 0, scale = 0.67)
## 
## Coefficients
##  ~ cauchy(location = [0,0,0,...], scale = [0.67,0.67,0.67,...])
##      **adjusted scale = [0.67,0.67,1.70,...]
## 
## Covariance
##  ~ decov(reg. = 1, conc. = 1, shape = 1, scale = 1)
## ------
## See help('prior_summary.stanreg') for more details
## Check ESS and Rhat
## Rhats all look good.  ESS a little low for grad years + some sigmas
model %>%
    summary() %>%
    as.data.frame() %>%
    rownames_to_column('parameter') %>%
    select(parameter, n_eff, Rhat) %>%
    # knitr::kable()
    ggplot(aes(n_eff, Rhat, label = parameter)) +
    geom_point() +
    geom_vline(xintercept = 3000) +
    geom_hline(yintercept = 1.01)

if (require(plotly)) {
    plotly::ggplotly()    
}
## Variables w/ fewer than 3000 effective draws
## covariance on random intercepts; log posterior
model %>% 
    summary() %>% 
    as.data.frame() %>% 
    rownames_to_column('parameter') %>% 
    as_tibble() %>% 
    filter(n_eff < 3000) %>% 
    select(parameter, n_eff)
## # A tibble: 2 x 2
##   parameter                                n_eff
##   <chr>                                    <dbl>
## 1 Sigma[community:(Intercept),(Intercept)]  1933
## 2 log-posterior                             1807
## Check predictions
pp_check(model, nreps = 200)

pp_check(model, nreps = 200, plotfun = 'ppc_bars')

## <https://arxiv.org/pdf/1605.01311.pdf>
pp_check(model, nreps = 200, plotfun = 'ppc_rootogram')

pp_check(model, nreps = 200, plotfun = 'ppc_rootogram', 
         style = 'hanging')

## 90% centered posterior intervals
estimates = posterior_estimates(model, prob = .9)

## Estimates plot
estimates %>% 
    filter(entity != 'intercept', 
           group != 'placement_year') %>% 
    ## posterior_estimates() already exponentiates estimates
    mutate_if(is.numeric, ~ . - 1) %>% 
    ggplot(aes(x = level, y = estimate, 
           ymin = lower, ymax = upper, 
           color = group)) +
    geom_hline(yintercept = 0, linetype = 'dashed') +
    geom_pointrange() + 
    scale_color_viridis_d(name = 'covariate\ngroup') +
    xlab('') + #ylab('') +
    scale_y_continuous(labels = scales::percent_format(), 
                       name = '') +
    coord_flip(ylim = c(-1, 1.75)) +
    facet_wrap(~ entity, scales = 'free') +
    theme(legend.position = 'bottom')

ggsave(str_c(output_folder, 'estimates.png'), 
       width = 8, height = 4.5, 
       scale = 1.5)
ggsave(str_c(paper_folder, 'fig_reg_estimates.png'), 
       width = 8, height = 4.5, 
       scale = 1.5)

estimates %>% 
    filter(entity != 'intercept', 
           group != 'placement_year') %>% 
    select(group, level, estimate, lower, upper) %>% 
    mutate_if(is.factor, as.character) %>% 
    arrange(group, level) %>% 
    knitr::kable(format = 'latex', 
                 digits = 2,
                 booktabs = TRUE, 
                 label = 'estimates', 
                 caption = 'Estimated regression coefficients.  Lower and upper columns give the left and right endpoints, respectively, of the centered 90\\% posterior intervals.') %>% 
    write_file(path = str_c(output_folder, 'estimates.tex'))


## Marginal effects for gender and prestige ----
## <https://stackoverflow.com/questions/45037485/calculating-marginal-effects-in-binomial-logit-using-rstanarm>
marginals = function (dataf, model, variable, 
                      ref_value = 0L, 
                      alt_value = 1L) {
    variable = enquo(variable)
    
    all_0 = mutate(dataf, !!variable := ref_value)
    all_1 = mutate(dataf, !!variable := alt_value)
    
    pred_0 = posterior_linpred(model, newdata = all_0, 
                               transform = TRUE)
    pred_1 = posterior_linpred(model, newdata = all_1, 
                               transform = TRUE)
    
    marginal_effect = pred_1 - pred_0
    return(marginal_effect)
}

marginals_gender = individual_df %>% 
    ## posterior_linpred raises an error when there are any NAs, even in columns that aren't used by the model
    select(-city, -state) %>% 
    marginals(model, gender, 
              ref_value = 'm', 
              alt_value = 'w')

apply(marginals_gender, 1, mean) %>% 
    quantile(probs = c(.05, .5, .95))
##         5%        50%        95% 
## 0.06521784 0.10415260 0.14256224
#         5%        50%        95% 
# 0.06891015 0.10920815 0.14868667


marginals_prestige = individual_df %>% 
    select(-city, -state) %>% 
    marginals(model, prestige, 'low-prestige', 'high-prestige')

apply(marginals_prestige, 1, mean) %>% 
    quantile(probs = c(.05, .5, .95))
##         5%        50%        95% 
## 0.07925371 0.12297629 0.16722014
#          5%        50%        95% 
# 0.07614823 0.11987722 0.16543114 

marginals_canada = individual_df %>% 
    select(-city, -state) %>% 
    marginals(model, country, 'U.S.', 'Canada') %>% 
    apply(1, mean) %>% 
    quantile(probs = c(.05, .5, .95))


## Schools in certain communities ----
comms_of_interest = c(3, 5, 12, 37, 54, 
                         8, 27, 38, 43) %>% 
    as.character()

univ_df %>% 
    filter(community %in% comms_of_interest, 
           total_placements > 0) %>% 
    select(community, name = univ_name, 
           total_placements, perm_placement_rate) %>% 
    mutate(community = fct_relevel(community, comms_of_interest), 
           perm_placement_rate = scales::percent_format()(perm_placement_rate)) %>% 
    arrange(community, name) %>% 
    knitr::kable(format = 'latex', 
                 # digits = 2,
                 booktabs = TRUE, 
                 label = 'comms', 
                 caption = 'Universities in selected topological communities.  Only universities with at least 1 placement in the data are shown.') %>% 
    write_file(path = str_c(output_folder, 'comms.tex'))


sessionInfo()
## R version 3.5.1 (2018-07-02)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS  10.14.6
## 
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] plotly_4.8.0     assertthat_0.2.0 tictoc_1.0       rstanarm_2.18.2 
##  [5] Rcpp_1.0.1       broom_0.5.2      cowplot_1.0.0    forcats_0.4.0   
##  [9] stringr_1.4.0    dplyr_0.8.2      purrr_0.3.2      readr_1.3.1     
## [13] tidyr_0.8.3      tibble_2.1.3     ggplot2_3.2.0    tidyverse_1.2.1 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-137       matrixStats_0.54.0 xts_0.11-2        
##  [4] lubridate_1.7.4    RColorBrewer_1.1-2 threejs_0.3.1     
##  [7] httr_1.4.0         rstan_2.18.2       tools_3.5.1       
## [10] backports_1.1.3    utf8_1.1.4         R6_2.4.0          
## [13] DT_0.5             lazyeval_0.2.1     colorspace_1.4-0  
## [16] withr_2.1.2        tidyselect_0.2.5   gridExtra_2.3     
## [19] prettyunits_1.0.2  processx_3.3.0     compiler_3.5.1    
## [22] cli_1.1.0          rvest_0.3.4        xml2_1.2.0        
## [25] shinyjs_1.0        labeling_0.3       colourpicker_1.0  
## [28] scales_1.0.0       dygraphs_1.1.1.6   ggridges_0.5.1    
## [31] callr_3.2.0        digest_0.6.18      StanHeaders_2.18.1
## [34] minqa_1.2.4        rmarkdown_1.12     base64enc_0.1-3   
## [37] pkgconfig_2.0.2    htmltools_0.3.6    lme4_1.1-21       
## [40] highr_0.7          htmlwidgets_1.3    rlang_0.4.0       
## [43] readxl_1.3.1       rstudioapi_0.10    shiny_1.2.0       
## [46] generics_0.0.2     zoo_1.8-4          jsonlite_1.6      
## [49] crosstalk_1.0.0    gtools_3.8.1       inline_0.3.15     
## [52] magrittr_1.5       loo_2.1.0          bayesplot_1.6.0   
## [55] Matrix_1.2-17      fansi_0.4.0        munsell_0.5.0     
## [58] stringi_1.4.3      yaml_2.2.0         MASS_7.3-51.1     
## [61] pkgbuild_1.0.2     plyr_1.8.4         grid_3.5.1        
## [64] parallel_3.5.1     promises_1.0.1     crayon_1.3.4      
## [67] miniUI_0.1.1.1     lattice_0.20-38    splines_3.5.1     
## [70] haven_2.1.0        hms_0.4.2          knitr_1.22        
## [73] ps_1.3.0           pillar_1.3.1       igraph_1.2.4      
## [76] boot_1.3-20        markdown_0.9       shinystan_2.5.0   
## [79] codetools_0.2-16   reshape2_1.4.3     stats4_3.5.1      
## [82] rstantools_1.5.1   glue_1.3.1         evaluate_0.13     
## [85] data.table_1.12.0  modelr_0.1.4       nloptr_1.2.1      
## [88] httpuv_1.4.5.1     cellranger_1.1.0   gtable_0.2.0      
## [91] xfun_0.5           mime_0.6           xtable_1.8-3      
## [94] later_0.8.0        viridisLite_0.3.0  survival_2.43-3   
## [97] rsconnect_0.8.15   shinythemes_1.1.2